Question

Integrate
by using a suitable substitution:-

(a) $\int \frac{3}{{\left(2-x\right)}^2}dx$

(b) $\int sin\left(8z-5\right)dz$

Answer 1

a) $\int \frac{3}{(2-x{)}^2}dx$

$2-x=t$

$-dx=dt$

$3\int \frac{-dt}{t^2}$

$-3\int \frac{dt}{t^2}$

$\frac{3}{t}+C$

$\frac{3}{(2-x)}+C$(Ans)

b) $\int \sin (8z-5)dz$

$8z-5=t$

$8dz=dt$

$dz=\frac{1}{8}dt$

= $\frac{1}{8}\int \sin tdt$

= $\frac{-1}{8}\cos t+C=\frac{-1}{8}\cos (8z-5)+C$